Carry out the row operation on the matrix. 9 8 7 4 56 R1 – R2 → R1 on 60
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
8.
![**Matrix Row Operation Explanation**
**Objective:**
Carry out the row operation on the matrix.
**Operation:**
\( R_1 - R_2 \rightarrow R_1 \)
**Initial Matrix:**
\[
\begin{pmatrix}
9 & 8 & \vert & 56 \\
7 & 4 & \vert & 60
\end{pmatrix}
\]
**Steps:**
1. Subtract the elements of Row 2 from the corresponding elements in Row 1.
- For the first column: \( 9 - 7 = 2 \)
- For the second column: \( 8 - 4 = 4 \)
- For the third column (right side of the vertical line): \( 56 - 60 = -4 \)
**Resulting Matrix:**
\[
\begin{pmatrix}
2 & 4 & \vert & -4 \\
7 & 4 & \vert & 60
\end{pmatrix}
\]
**Explanation:**
The operation performed replaces the original Row 1 with the difference between Row 1 and Row 2. The vertical bar within the matrix generally represents the separation between the coefficients on the left and the constants on the right, typically used in augmented matrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d8e838a-6c8b-4033-a5e3-a56465c5aa54%2F2cd07913-ba92-4455-a9b9-58bc10ef8c11%2Fyhlly2_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Row Operation Explanation**
**Objective:**
Carry out the row operation on the matrix.
**Operation:**
\( R_1 - R_2 \rightarrow R_1 \)
**Initial Matrix:**
\[
\begin{pmatrix}
9 & 8 & \vert & 56 \\
7 & 4 & \vert & 60
\end{pmatrix}
\]
**Steps:**
1. Subtract the elements of Row 2 from the corresponding elements in Row 1.
- For the first column: \( 9 - 7 = 2 \)
- For the second column: \( 8 - 4 = 4 \)
- For the third column (right side of the vertical line): \( 56 - 60 = -4 \)
**Resulting Matrix:**
\[
\begin{pmatrix}
2 & 4 & \vert & -4 \\
7 & 4 & \vert & 60
\end{pmatrix}
\]
**Explanation:**
The operation performed replaces the original Row 1 with the difference between Row 1 and Row 2. The vertical bar within the matrix generally represents the separation between the coefficients on the left and the constants on the right, typically used in augmented matrices.
Expert Solution
Step 1
Given matrix is
To apply the below row operation on the above matrix.
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